Problem: $A$ $B$ $C$ If: $ AB = 8x + 7$, $ BC = 2x + 7$, and $ AC = 24$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 7} + {2x + 7} = {24}$ Combine like terms: $ 10x + 14 = {24}$ Subtract $14$ from both sides: $ 10x = 10$ Divide both sides by $10$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 2({1}) + 7$ Simplify: $ {BC = 2 + 7}$ Simplify to find ${BC}$ : $ {BC = 9}$